Abstract
We consider a stochastic model of infection spread on the complete graph on $N$ vertices incorporating dynamic partnerships, which we assume to be monogamous. This can be seen as a variation on the contact process in which some form of edge dynamics determines the set of contacts at each moment in time. We identify a basic reproduction number $R_{0}$ with the property that if $R_{0}<1$ the infection dies out by time $O(\log N)$, while if $R_{0}>1$ the infection survives for an amount of time $e^{\gamma N}$ for some $\gamma>0$ and hovers around a uniquely determined metastable proportion of infectious individuals. The proof in both cases relies on comparison to a set of mean-field equations when the infection is widespread, and to a branching process when the infection is sparse.
Citation
Eric Foxall. Roderick Edwards. P. van den Driessche. "Social contact processes and the partner model." Ann. Appl. Probab. 26 (3) 1297 - 1328, June 2016. https://doi.org/10.1214/15-AAP1117
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